Moving an animated / rigged object
Do it by make your armature an Root bone.
1. Select your Armature

2. Press Tab to enter Edit Mode

3. Press Shift + A To add new bone. Name it Root or whatever you want

4. Parent your current Root bone (which mean if you move it, the whole armature will move with it) to your new Root bone you just add.
Select your current Root bone, then Hold Shift and select new Root bone.
Press Ctrl + P then select Keep Offset
  
5. Now you can move your new bone to the origin and whole armature will go with that.